SOMA News 10 july 2016 E-Mail.

# Distribution of SOMA solutions.

We all assume that puzzling and finding solutions are things that happen, more or less by chance - some times Inspired like the sentence of a movie I saw "Chance favours a prepared mind"
Never the less, no predestination. - But is that true ?

Follow the question down these lines:

On 2015-07-27
Hi Thorleif
We were sitting around thinking about all 240 solutions to soma cube. Some questions arose.

1. Are some solutions more difficult to find?
2. If so, why would that be?
3. If 100 people were given a Soma cube to solve would there be a large number that were the same solution?
4. What does this potentially mean mathematically?

Thanks for your thoughts on this.
Thanks for being there.
All the best.

Marie and Petey

The same day
Subject: SOMA (Solution distribution)

Hi Marie and Petey

You actually touch on a subject that has not been examined.
So the only answer that I can provide is really just my own thoughts about the matter.

1. Are some solutions more difficult to find?
The immediate answer should be no, because each solution use the same pieces etc.etc.
On the other hand, if we look at the solution pattern, we findt that ie... the number of solutions that have "T" at an edge, are much larger than some other. And especially that V cannot occupy an edge. Saying that if a strategy starts with the same pieces, then some solutions are harder to find than others. Primarily because the player has to abandon a starting strategy and invent another before reaching the solution path.

2. If so, why would that be?
But I also strongly suspect that the real answer is yes, some are more difficult than others.
The reason being that people have a tendency to pick the A,B,P and V pieces last. Starting off using the L,Z,T.
When they do that, the solutions having L,Z or T at the rear edge, will be easier to find.

3. If 100 people were given a Soma cube to solve would there be a large number that were the same solution?
Yes, probably, as I said, people have a tendency to start with the flat pieces, so that would make the probabilities shift towads solution with such a piece at an edge..
On the other hand, a strategy of starting with A, B or P - and then flat pieces - is also effective, and if the players realize that fact, then we get a different distribution.

4. What does this potentially mean mathematically?
Oh well - yes..... ... that a good question...
That question no 4 is an immediate follow, from the other questions.
But in my opinion:
As the solution distribution connects to peoples indivitual skills, starting strategy, and the ability to realize a solution "path". Then any mathematics would be predominantly based on trials and statistics.

I hope my mix of thoughts was to some kind of help, probably realising the difficulty of the question.
And finally - Thank you for your kind words :o)
Friendliest Thorleif

The next day
Thank you for your super fast and informative response.
I think Petey ( the real mathematician) will be working on this for a science fair experiment. So you might hear from him again!
My job will be the construction of many soma cubes!

Thanks again.
Marie

Also on letter day 2

Hi Marie
That sound interesting - I am always interested in new ways of ideas.
So he shall be welcome to mail me some info.

And also 'if possible' some foto's showing puzzling people, to accompain the description.

I Will look forward to hearing from you again.

Friendliest, Thorleif Bundgaard

It seemed to stop there, BUT the question still stand.
How does solving puzzles like SOMA progress.?
What factors are helping or limiting our trials in solving a figure.?

Well it did'nt stop yet as I got an answer to my new email.

Jul 3, 2017 I wrote:
1. Did the project continue ??
2. What was the outcome ??
3. Did Petey work on it for the Science fair.
And finally.
4. If anything (even partially) came from this, like ie. a report, slide show, or such.
Then I would very much like to publish it in the Web newsletter.
Friendliest Thorleif

Jul 26, 2017 The answer was:
Thanks for writing.
Petey worked on a microbiology project instead last year.
Your email has given new life to the soma cube question.
He will probably get started this September on the great soma cube experiment. Will keep in touch!
Yours in mathy science - Peter Nicholas

SO, Now we just have to wait and see.
If any one out there have interest and capability to investigate this question,
then you are welcome to write to me.

By 2020-06-10 Bob Nungester made an investigation into various ways of depicting SOMA solutions.
Leading to various drawings and calculations, his figure in The new Radial SOMA graph give us
an insight into the connection of solutions.
And as Bob writes "... if you place piece 7 in one position vs. another your odds of finding some solution
will vary greatly. The placements that lead to only two or four solutions each will take much longer to solve
than the one that leads to about 93 different solutions. With that one just about any placement of the
remaining pieces will lead to some solution."